Shewhart and EWMA t control charts for short production runs

Short-run productions are common in manufacturing environments like job shops, which are characterized by a high degree of flexibility and production variety. Owing to the limited number of possible inspections during a short run, often the Phase I control chart cannot be performed and correct estimates for the population mean and standard deviation are not available. Thus, the hypothesis of known in-control population parameters cannot be assumed and the usual control chart statistics to monitor the sample mean are not applicable. t-charts have been recently proposed in the literature to protect against errors in population standard deviation estimation due to the limitation of available sampling measures. In this paper the t-charts are tested for implementation in short production runs to monitor the process mean and their statistical properties are evaluated. Statistical performance measures properly designed to test the chart sensitivity during short runs have been considered to compare the performance of Shewhart and EWMA t-charts. Two initial setup conditions for the short run fixing the population mean exactly equal to the process target or, alternatively, introducing an initial setup error influencing the statistic distribution have been modelled. The numerical study considers several out-of-control process operating conditions including one-step shifts for the population mean and/or standard deviation. The obtained results show that the t-charts can be successfully implemented to monitor a short run. Finally, an illustrative example is presented to show the use of the investigated t charts.